Band Theory & Unit Cells (9/25)

Describe the electron sea model.

Valence electrons are delocalized and free to move throughout the crystal.

Why do metals have the malleability and ductility properties that they have?

the behavior of mobile valence electrons

True/false: Molten states conduct electricity.

True

What is it called when molecular orbital theory is applied to crystals?

band theory

Draw the band theory model of 2s orbitals from two Li atoms interacting.

Draw the band theory model for four Li atoms interactions.

What is a band in band theory?

A bunch of atomic orbitals stacked on top of each other

What is band width? How do you calculate it?

The width of a continuous band. (Energy of highest atomic orbital) - (energy of lowest atomic orbital).

In the following image, which of these is weak bonding and which is strong bonding?

left is weak; right is strong

What does band gap depend on?

energy gap between AOs in the atom; widths of the bands

Which is bigger: the band gap or the atomic orbital gap?

atomic orbital gaps

Why do insulators have large band gaps?

They don’t conduct - mobile electrons have trouble jumping the bands to become mobile

What type of band gap do metallic conductors use?

What is the bottom band and what is the top band called?

bottom band: valence band; top band: conductive band

What is a major difference between conductors and semiconductors?

as temperature increase:

• conductors decrease conductivity

• semiconductors increase conductivity

What is doping?

adding a small impurity to a host metal to changes its behavior

What is the main difference between n-type and p-type doping?

n-type: dope valence electrons > host valence electrons

p-type: dope valence electrons < host valence electrons

They both increase conductivity.

Describe the impurity band of an n-type dope.

N-type doping adds more electrons and creates a negatively charged semiconductor.

Describe the impurity band of an p-type dope.

P-type bonding creates more holes where electrons should be and creates a positively charged semiconductor.

How is maximum attraction obtained?

each atom is surrounded by the largest possible number of other atoms

simple cubic: % efficiency?

52

simple cubic: coordination number

6

simple cubic: net atoms per unit cell

1

simple cubic: examples

po

simple cubic: e equation

e = 2r

body centered cubic: % efficiency

68

body centered cubic: net atoms per unit cell

2

body centered cubic: coordination number

8

body centered cubic: examples

Na, V, K, Fe (low temp)

body centered cubic: e equation

e = (4/root 3)r

face centered cubic: % efficiency

74

face centered cubic: net atoms per unit cell

4

face centered cubic: coordination number

12

face centered cubic: examples

Cu, Al, Ag, Au, Fe (high temp)

face centered cubic: e equation

e = (4/root 2)r

hexagonal close packing: % efficiency

74

hexagonal close packing: coordination number

12

hexagonal close packing: net atoms per unit cell

2

hexagonal close packing: examples

Mg, Ru, Co, Re, Os

Draw the unit cell for simple cubic.

Draw the unit cell for body centered cubic.

Draw the unit cell for face centered cubic.

Draw the unit cell for hexagonal close packing.